Find the arc length L of the graph of r(t). 1 .3 r(t) = i+t j+¬V61² k, 2 <153 L =

Q: Let f: R → R some function that is at least two times derivable , for f we know that f"(-1) = f"(2)…

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Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) = – 0.02q + 5q 38 where q is…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: We have to calculate volume of solid obtained by revolving the region enclosed by curves x=cosecy,…

Q: 1- Show that the following subset is a subgroup. H = {o e S, lo(n) = n}cS,

A: Explanation of the answer is as follows

Q: V4-x² c 3-x2-y² Evaluate the iterated integral. x dz dy dx -5+x²+y² A 128/15 в) 16/89 c) 23/6 6.

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Q: The Leslie matrix below describes a population with four age groups consisting of juveniles,…

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Q: Use Green Theorem to Evaluate y x²dx – x²dy where C is left half of x² + y² = 25 %3D

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Q: dx (x² – 1)²

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Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

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Q: Find the four​ second-order partial derivatives for​ f(x, ​y)= 7x4y8 + 8x7y5 Fxx= Fyy= Fxy= Fyx=

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Q: A property has been mapped, and the height above sea level is determined to be represented by the…

A: Given a scalar field representative of height.

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X + y +…

A: Here, to find the volume if the solid enclosed by: x2+y2+z2=4a2 The cartesian to spherical…

Q: Find the limit. lim (t i - 9 j+ 1? k) lim (t i – 9 j+ k) = i+ j+ k i i i

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Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

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Q: Evaluate JJ xy dA, where R is the region in (1, 3) (5, 3) (2, 1) (4, 1)

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Q: Find the exact sülution fur ylz Xtzy

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Q: 2.1 Find the value of x and y from the given complex equation (-2 + i)x + 2y =1+ 3i. 2.2 Write the…

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Q: Consider the curve (y2 = 9 +x) that defines y as an implicit function of x. If P (xo, yo) is the…

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Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 17 tan Р(-18, 18); а %3D…

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Q: 0, 1, 2, 3, and 4 about x = xo Find the Taylor polynomials of orders n = and then find the nth…

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Q: View Policies Current Attempt in Progress Find the area of the region inside the circle r = 30 sin 0…

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Q: 3.1 If the Laplace transform of coswt is then find the Laplace Transform of the s2+w? following…

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Q: Find the area of the region using a double integral. The region bounded by y = 2x³, 2x + y = 4, and…

A: To find the area of the region using a double integral.The region bounded by y=2x3, 2x+y=4, and the…

Q: Question 19 Evaluate JJ xy dA , where R is the region in ´(1, 3) (5, 3) R (2, 1) (4, 1) х А) 56 В)…

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Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

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Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

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Q: dy y+1 2.

A: Integrate as general

Q: 4. Show that a b

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Q: Use the derivative of the function shown below to determine the open intervals in which the function…

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Q: Find the area of the region inside the circle r = 12sinθ and outside the cardioid r = 4 + 4 sinθ.

A: Area

Q: Use the properties of the derivative to find the following. r(t) = ti + 4tj + t?k, u(t) = 4ti + t²j…

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Q: d d Calculate r:(t) · r2(t)] and r:(t) × r2(t)] first by differentiating dt dt the product directly…

A: r1(t)=cos(t)i+sin(t)j+3t kr2(t)=2 i+t k

Q: r = V cos 20 r = 5 cos 0

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Q: Multiply. 4x 27x +9 12x + 4

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Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

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Q: A torus is formed by revolving the region bounded by the circle x² + y² = 9 about the line x = 5…

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Q: Determine the general solution to the vector differential equation r' = Ax with A = [2030-40 -30 2]…

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Q: Find the exact arc length of the curve over the stated interval. 1 1 + from y = 1 to y = 3 x = NOTE:…

A: Aec length of the given curveL=∫131+dxdy2dy    Considerx=16y3+12y-1thendxdy=(16×3y2)+-12y2…

Q: Sketch the region enclosed by the curves and find its area. y = cos8x, y = 0, x = π/16, x = π/8

A: Given: y = cos8x, y = 0, x = π/16, x = π/8

Q: Find the area of the region inside the circle r = 18sinθ and outside the cardioid r = 6 + 6 sinθ.

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Q: 4. Under the usual addition 47Z/2021Z .

A: A detailed solution is given below.

Q: 324-y' y dx dy 18

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Q: Sand falls from a conveyor belt at a rate of 10 m^3/min and accumulate in a conical pile with the…

A: Use derivative concept

Q: Consider a field with V = 8a²y² î + 4y²j + –5y² z³k a) Find the divergence of V: V•V: b) Find the…

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Q: a) Consider the scalar function: f(x, y) = -4x*y³ – 2a*y? Find the gradient: Vf(x, y) = i+ Find the…

A: Given; f(x,y)=-4x^2y^3-2x^4y^2

Q: Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2 + y?, below…

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Q: Find the area of the region inside the circle r = 30 sin 0 and outside the cardioid r = 10+ 10 sin…

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Q: If g(x) J.J S. 1 -dt , find g'(2).

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Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A: We have to find the equation of population.

Q: The general solution of y² + x² ªY dx xyis dx

A: This is a homogeneous differential equation which can be solved by putting y=vx